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A: According to the guidelines I need to answer only first three parts still I have solved first four…
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Q: simplified
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A: Observe the graph and answer.
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A: Please refer to the image below
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- Let F(x, y, z) =⟨3x2y+az, x3,3x+ 3z2⟩ be a vector field. For what values of a is F conservative?Let V = span (sint , cost) over R. Does the derivative map of into itself, have any nonzero eigenvectors in ? If so, which?Show that the outward flux of a constant vector field across any closed surface to which the Divergence Theorem applies is zero.
- linearise R = AT + BT2Evaluate the work done between point 1 and point 2 for the conservative field F.F = 6x i + 6y j + 6z k; P 1(4, 3, 5) , P 2(5, 6, 7) a)W = 180 b) W = 480 c) W = 0 d) W = - 180what local linearizatoin of the function f(x,y) sin(xy) + cos(x/y) at (pie/4, 1) (show all steps please)
- Suppose that f and g are Riemann integrable functions on [a, b].Investigate the conversion of transfer functions to zero-pole diagrams7. (a) Determine the value of k for which (u, v, w) is an orthogonal coordinate system ifx = −(u2 + kv2), y = uv and z = w.(b) Given that F and G are vector fields with G a vector potential of F, prove that G is notunique.(c) Show that a vector field F =(4uv − θ3/√u2 + v2, 2u2/√u2 + v2, (lnθ − 3uθ2/uv), defined in paraboloidalcoordinate system (x = uv cos θ, y = uv sin θ, z =1/2(u2 − v2) is irrotational and hence find its scalar potential.